Explore >> Select a destination
|
You are here 
|
ckrao.wordpress.com | ||
| | | | |
algorithmsoup.wordpress.com
|
|
| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
| | | | |
statisticaloddsandends.wordpress.com
|
|
| | | | | If $latex Z_1, \dots, Z_n$ are independent $latex \text{Cauchy}(0, 1)$ variables and $latex w= (w_1, \dots, w_n)$ is a random vector independent of the $latex Z_i$'s with $latex w_i \geq 0$ for all $latex i$ and $latex w_1 + \dots w_n = 0$, it is well-known that $latex \displaystyle\sum_{i=1}^n w_i Z_i$ also has a $latex... | |
| | | | |
mikespivey.wordpress.com
|
|
| | | | | It's fairly well-known, to those who know it, that $latex \displaystyle \left(\sum_{k=1}^n k \right)^2 = \frac{n^2(n+1)^2}{4} = \sum_{k=1}^n k^3 $. In other words, the square of the sum of the first n positive integers equals the sum of the cubes of the first n positive integers. It's probably less well-known that a similar relationship holds... | |
| | | | |
thisfineplace.wordpress.com
|
|
| | | Don't just escape from something; escape to something. Chris Guillebeau | ||
